English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

We revisit the classical theory of stochastic integral convergence onSkorokhod space, providing a new comprehensive treatment under Skorokhod's J1and M1 topologies based on a simple and tractable notion of good decompositionsfor the integrators. Our analysis yields new insights even in the classical J1setting and addresses the sharpness of various key statements. As regardsconvergence of stochastic integrals in the M1 setting, our contribution istwofold. On the one hand, we derive useful sufficient conditions. On the otherhand, we demonstrate the failure of general weak continuity results forstrictly M1 convergent integrators. Closely related to this, we provide animportant structural result for local martingales on Skorokhod space, showingthat their M1 tightness generally implies their J1 tightness. The practicalityof our results is illustrated through novel contributions to applications fromeconometrics, statistical mechanics, mathematical finance, and insurancemathematics.

Weak Convergence of Stochastic Integrals on Skorokhod Space in Skorokhod's J1 and M1 Topologies